THE ROTATION OF A NON-RIGID, NON-SYMMETRICAL EARTH II: FREE NUTATIONS AND DISSIPATIVE EFFECTS JUAN GETINO 1 , ANA B. GONZÁLEZ 2 and ALBERTO ESCAPA 1 1 Grupo de Mecánica Celeste, Departamento de Matemática Aplicada Fundamental, Facultad de Ciencias, Universidad de Valladolid, Prado de la Magdalena s/n, 47005 Valladolid, Spain 2 Grupo de Mecánica Celeste, Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, Paseo del Cauce s/n, 47011 Valladolid, Spain (Received: 8 April 1999; accepted: 10 March 2000) Abstract. The study of the rotation of a non-rigid, non-symmetrical Earth with a heterogeneous and stratified liquid core was recently accomplished by González and Getino (1997) through the Hamiltonian formalism. In this work that model is extended by including the effect of the dissip- ation arising from the mantle–core interaction due to the viscous and electromagnetic coupling. A canonical transformation to a new set of non-singular variables is performed, in order to avoid small divisors in the system of equations. Numerical estimations of the effect of the dissipation are given in form of tables and graphics, and the significance of this effect is discussed. Keywords: non-rigid earth, nutation, free nutation, dissipative effects 1. Introduction The Hamiltonian theory of Kinoshita (1977) of the rigid Earth has been extended by Getino (1995a, b) and Getino and Ferrándiz (1995, 1997) for non-rigid Earth models, considering the elasticity of the mantle, the presence of the fluid core and the solid inner core, and dissipation in the boundaries, with a canonical formulation by means of an adequate sets of Andoyer-like variables for the different layers. These works, as well as most of theories of rigid and non-rigid Earth consider a simplified symmetrical model, with A = B (principal moments of inertia). Nevertheless, the accuracy of the present observational data reached by modern techniques such as VLBI (very long baseline interferometry) and LLR (lunar laser ranging) requires to elaborate more precise rotation theories considering more realistic Earth models, and adding effects which were disregarded in the past. For instance, we can refer to the work by Kinoshita and Souchay (1990), which consider the triaxiality of the Earth among other effects. For this reason, González and Getino have recently begun the study of the effect of the triaxiality on the Earth’s rotation by extending the previous models of Getino (1995a, b) and Getino and Ferrándiz (1995, 1997) to the case A  = B . Still under the Hamiltonian formalism, the first paper (González and Getino, 1997) was devoted to the formulation of the free motion of a non-symmetrical Earth composed of a Celestial Mechanics and Dynamical Astronomy 76: 1–21, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.